Use a sign analysis to solve the following inequality #2x^3 < x^2+3x#? .

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Feb 9, 2018

Answer:

#]-oo, -3/2[uu]0,3[#

Explanation:

#2x^3 < x^2+3x#

#2x^3 - x^2-3x<0#

#x(2x^2 - x-3)<0#


#x=(-1+-sqrt(1-4*2*(-3)))/4#

#x=(-1+-sqrt(25))/4#

#x=(-1+-5)/4#

#x=-1 or x=-3/2#

The second-degree polynomial will be negative in# ]-3/2,-1[#


#color(white)(...........)-oo.....-3/2......-1........0............#
#xcolor(white)(...--)---------0++++++++#
#polynomial color(white)(.)+++0color(white)(.)--0+++++#
#gives color(white)(.)-----0color(white)(.)++0--0+++++#

#]-oo, -3/2[uu]0, +oo[#

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